Okay, there's a couple of other solutions to this. They're all very good solutions, but when it came time to do this myself I found it super easy to do using the same method you use to get the garbage dumpster achievement.
Here's what I did: after jumping inside the boat, grab onto the edge of the boat on the side facing the direction you want to travel. Then all you have to do is jump! Keep jumping and holding onto the edge of the boat. Make sure you don't go overboard (literally) by doing it constantly, or else you might have trouble getting back in. But as long as you hold onto the edge, you should be okay.
If you want to change direction, simply let go of the edge and pick a different side. You can pretty much ignore the oars, as they're pretty useless and can send you off course if you don't make good contact on the water on both sides of the boat.
Just grab the sides and jump!
Here's a video of when I got this:
I found this faster and easier to control than to try using the oars. (It's also easier to use than the speed boat, but for achievement purposes you wouldn't want to use that anyway.)
Now, just keep jumping towards the tanker, and the row boat will eventually get there. Once you reach the side of the tanker, the achievement will pop.